论文标题
无限双覆盖地图的反转
Inversion of the Indefinite Double Covering Map
论文作者
论文摘要
提出了针对无限双覆盖图的明确反转算法方法。这些基于给定基质的givens分解或具有签名的适当无限正交组中给定基质的极性分解（p，q）。作为副产品，我们确定覆盖组的前图，即适当的无限正交组中的正矩阵，本身可以被选为积极的确定性。反转等于在几个变量中求解多项式系统。我们的方法通过检查，groebner碱基或反转相关的代数同构和明确计算某些指数来解决该系统。当与givens分解一起使用时，最后一个方法将对所有（P，Q）进行完全构建的扩展。其余方法需要覆盖地图的矩阵形式的详细信息，但随后提供有关预映射的更多信息。该技术在{（2,1），（2,2），（3,2），（4,1）}中的（P，Q）中进行了说明。
Algorithmic methods for the explicit inversion of the indefinite double covering maps are proposed. These are based on either the Givens decomposition or the polar decomposition of the given matrix in the proper, indefinite orthogonal group with signature (p,q). As a by-product we establish that the preimage in the covering group, of a positive matrix in the proper, indefinite orthogonal group, can itself be chosen to be positive definite. Inversion amounts to solving a polynomial system in several variables. Our methods solve this system by either inspection, Groebner bases or by inverting the associated Lie algebra isomorphism and computing certain exponentials explicitly. The last method extends fully constructively for all (p,q) when used together with Givens decompositions. The remaining methods require details of the matrix form of the covering map, but then provide more information about the preimage. The techniques are illustrated for (p, q)in {(2,1), (2,2), (3,2), (4,1)}.
